An analytical model for small signal stability analysis in unbalanced electrical power systems

Humberto Verdejo, Pablo Moreira, Wolfgang Kliemann, Cristhian Becker, José Delpiano

Research output: Contribution to journalArticlepeer-review


This paper presents a general model to carry out a small signal stability analysis in electrical power systems (EPSs) that operate in unbalanced conditions. The classic traditional approach is based on a phase representation where it is supposed that the triphasic electric grid does not suffer any variations during its operation. With the presence of unbalances in transmission lines and loads, it is necessary to develop a general model that allows answering the needs and challenges with which modern electric systems must deal. The present work firstly intends to address the three-phase representation of an EPS, including the controllers. The proposed model is applied to a classical test system, a three machine-nine bus system, considering all the dynamic and algebraic variations associated with angular stability analysis. The proposed approach to small signal stability analysis shows results that differ from the classical analysis. The results are backed up with time domain simulations, and therefore, these results could be used in the calculation of the controllers that operate in unbalanced multimachine systems.

Original languageEnglish
Article number8855
Pages (from-to)1-28
Number of pages28
JournalApplied Sciences (Switzerland)
Issue number24
StatePublished - 2 Dec 2020
Externally publishedYes


  • Power system modeling
  • Small signal stability
  • Unbalanced conditions

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